The brute-force attack time against a passkey depends on entropy and attack rate:
\[T_{attack} = \frac{2^{entropy}}{R_{attempts}} \times 0.5\]
where \(R_{attempts}\) is the number of pairing attempts per second (factor 0.5 assumes average case).
Example: A 6-digit PIN (000000-999999) provides: - Entropy: \(\log_2(1,000,000) = 19.93\) bits - If attacker attempts 10 pairings/second: \(T_{attack} = \frac{2^{19.93}}{10} \times 0.5 = \frac{1,000,000}{10} \times 0.5 = 50,000\) seconds ≈ 13.9 hours
For LE Secure Connections with rate limiting (1 attempt per 30 seconds after 3 failures): - Effective rate: 0.033 attempts/second - \(T_{attack} = \frac{1,000,000}{0.033} \times 0.5 \approx 15,000,000\) seconds ≈ 174 days
Rate limiting transforms a 14-hour attack into a 174-day attack, making brute force impractical. This is why BLE devices MUST implement retry delays.